Praise be to Allah.
We ask Allah to reward you for your eagerness to pray in congregation, and for your efforts to do so regularly. We ask Him to enable you to do all that is good.
It should be noted that you are dealing with a Lord Who is generous, kind and merciful; He is more merciful towards His slaves than they are to themselves. He is watching over your heart and He knows what is on your mind. If He sees that your intention is sincere, He will decree the reward for you in full, and He will overlook every mistake and shortcoming.
Sharee’ah excuses the one who falls asleep, if he misses prayer in congregation or he misses the time of prayer altogether, so long as he availed himself of the appropriate means and tried hard to catch up with the prayer in congregation. If sleep overtook him after that because of something that was beyond his control, without any shortcoming or negligence on his part, then Allah will forgive him, for He does not burden any soul beyond its scope.
Al-Bukhaari (570) and Muslim (681) narrated from Abu Qataadah (may Allah be pleased with him) that the Prophet (peace and blessings of Allah be upon him) was with some of his companions on a journey, and they halted at the end of the night. He lay down his head, then he said: “Guard our prayer for us.” The first one to wake up was the Messenger of Allah (peace and blessings of Allah be upon him). When the sun was on his back. We woke up, startled, then he said, “Ride on.” So we rode on and traveled until the sun had risen, then he stopped and called for the water vessel I had with me, in which there was a little water. He did wudoo’ from it, using less water than usual. A little water was left in it, and he said to Abu Qataadah, “Guard your water vessel, for you will see something happen with it.” Then Bilaal gave the call to prayer and the Messenger of Allah (peace and blessings of Allah be upon him) prayed two rak’ahs, then he prayed Fajr, and did as he did every day. The Messenger of Allah (peace and blessings of Allah be upon him) rode on and we rode with him, and we began to whisper to one another, saying: What expiation is there for what we have done by neglecting our prayer? Then he said: “Do you not have an example in me?” Then he said: “There is no negligence in sleep, rather negligence is the fault of one who does not pray until the time for the next prayer comes. Whoever does that, let him pray when he remembers it, and if it is the following day, then let him pray at the time of the prayer (that he missed).”
Think about what the Prophet (peace and blessings of Allah be upon him) said to his companions: “Guard our prayer for us.” You will see that it indicates that it is essential to take the necessary means to offer prayer on time and to pray in congregation, but the effort and exhaustion caused by travel prevented them from waking up at the time of Fajr, and they only woke up when the sun has risen, so they had an excuse in that case.
Al-Nawawi said in Sharh Muslim (5/186):
This is evidence for that on which the scholars are unanimously agreed, that the sleeper is not accountable. End quote.
It says in al-Mawsoo’ah al-Fiqhiyyah (7/187):
It may be understood from this hadeeth that if a person thinks it most likely that if he sleeps he will miss the prayer, he should tell someone to wake him up. End quote.
To sum up: If you need to sleep before the prayer but are keen to wake up, and you tell someone in your family to wake you up, or you set an alarm clock, there is nothing wrong with that, and the Muslim is not sinning if he misses prayer in congregation or misses the time for prayer (in that case).
As for the vow you made, you should have fulfilled it. As you did not do that, you have to offer the expiation for breaking an oath (kafaarat yameen), because the Prophet (peace and blessings of Allah be upon him) said: “The expiation for breaking a vow is kafaarat yameen.” Narrated by Muslim (1645). You only have to offer one expiation, even if there were many days on which you slept before ‘Asr, because the vow is dissolved when it is broken and it does not remain in effect.
Kafaarat yameen is freeing a slave or feeding ten poor persons with the average kind of food that you eat, or clothing them. If you cannot do one of these three things, then you have to fast for three days.
See also the answer to question no. 45676
And Allah knows best.